// Copyright © 2021 siddharth ravikumar <s@ricketyspace.net>
// SPDX-License-Identifier: ISC
package lib
import (
"math/big"
)
// Cube root tolerance.
var bigCubeRootTolerance = big.NewFloat(0.00001)
// Returns cube root of a.
//
// Uses Newton's method.
// https://en.wikipedia.org/wiki/Newton's_method
func BigCubeRoot(a *big.Float) *big.Float {
// If x^3 = a, then our f(x) is:
// f(x) = x^3 - a
fx := func(x *big.Float) *big.Float {
// x^3
e := big.NewFloat(0)
e = e.Mul(x, x)
e = e.Mul(e, x)
// x^3 - a
z := big.NewFloat(0).Sub(e, a)
return z
}
// f'(x) is:
// f'(x) = 3 * x^2
fxPrime := func(x *big.Float) *big.Float {
// x^2
x2 := big.NewFloat(0).Mul(x, x)
// 3 * x^2
z := big.NewFloat(0).Mul(big.NewFloat(3), x2)
return z
}
x0 := a // Initial guess.
for i := 0; i < 1000000; i++ {
// f(x0) / f'(x0)
d := fx(x0)
d = d.Quo(d, fxPrime(x0))
// x0 - ( f(x0) / f'(x0) )
x1 := big.NewFloat(0).Set(x0)
x1 = x1.Sub(x1, d)
// x0 - x1
df := big.NewFloat(0).Set(x0)
df = df.Sub(df, x1)
df = df.Abs(df)
if df.Cmp(bigCubeRootTolerance) == -1 {
return x1
}
x0 = x1
}
return nil
}
// Returns cube root of a.
//
// Uses Newton's method.
// https://en.wikipedia.org/wiki/Newton's_method
func BigIntCubeRoot(a *big.Int) *big.Int {
// If x^3 = a, then our f(x) is:
// f(x) = x^3 - a
fx := func(x *big.Int) *big.Int {
// x^3
e := big.NewInt(0)
e = e.Mul(x, x)
e = e.Mul(e, x)
// x^3 - a
z := big.NewInt(0).Sub(e, a)
return z
}
// f'(x) is:
// f'(x) = 3 * x^2
fxPrime := func(x *big.Int) *big.Int {
// x^2
x2 := big.NewInt(0).Mul(x, x)
// 3 * x^2
z := big.NewInt(0).Mul(big.NewInt(3), x2)
return z
}
x0 := a // Initial guess.
zero := big.NewInt(0)
one := big.NewInt(1)
for i := 0; i < 1000000; i++ {
// f(x0) / f'(x0)
d := fx(x0)
d = d.Div(d, fxPrime(x0))
// x0 - ( f(x0) / f'(x0) )
x1 := big.NewInt(0).Set(x0)
x1 = x1.Sub(x1, d)
// x0 - x1
df := big.NewInt(0).Set(x0)
df = df.Sub(df, x1)
df = df.Abs(df)
if df.Cmp(zero) == 0 {
return x1.Sub(x1, one)
}
x0 = x1
}
return nil
}
